Mark Holland scored the only goal in a 1-0 second-leg away win that followed a 1-1 draw at Windsor Park in Belfast.
Meanwhile, Eircom Premier League contenders Cork City earned a tie against Swedish outfit Hammarby with a 2-1 aggregate win against Valur.
The Irish side won 2-0 in Iceland, but were made to sweat at home in the second leg, as they went down 1-0 but still did enough.
The teams must successfully negotiate two more rounds to be among the 11 Intertoto teams who win a place in the second qualifying round of the UEFA Cup.
Llanelli were knocked out by Vetra of Lithuania after an extraordinary game at Richmond Park in Carmarthen.
Trailing 3-1 after the first leg, the Welsh side claimed a thrilling 5-3 victory in the return fixture, but the Baltic side went through on away goals.
Turkish side Trabzonspor, and former Champions League contenders Maccabi Haifa are among the sides taking part in the second round.
Second round matches will be played over two legs on July 7-8 and the following weekend.